After a half-hour spent cooling their heels and speculating which new diva was causing the delay of Fox’s “American Idol” Q&A session at Winter TV Press Tour 2013, critics finally got to ask Mariah Carey and Nicki Minaj whether the audition brawl leaked to TMZ in October was the real deal or a trumped-up gag to goose show ratings.

“We’re professionals. Have you ever had an argument with someone you’ve worked with?” said Minaj, dressed in a pretty beige, clingy dress and Louboutin heels so high she had to be walked to her seat onstage.

One day after ABC News aired Babs Walters’s interview with Carey — in which she reiterated a claim she made in October about hiring a bodyguard to protect her from Minaj’s camp — Carey told TV critics: “The fighting is what it is. This is ‘American Idol.’ It’s bigger than . . . some stupid trumped-up thing” that was distracting from the singers and not fair to them.

Yet, interjected Minaj, every time she tries to talk about the contestants to reporters, they insist on pulling her back into conversation about the feud, the tape and TMZ.

Yeah — poor Nicki.

One critic asked each woman to say something nice about the other. While the crowd held their breath, Minaj began, calling Carey one of her favorite all-time artists and the shaper of a generation of singers.

Carey seemed to have more trouble talking about something other than herself but eventually got around to talking about working with Minaj on a single and realizing that Minaj was an artist who would go far. That single: “Up Out My Face.” Carey called the title “ironic.”

One critic wondered how they came to kiss and make up.

“I put on my sex tape,” Minaj responded.

“And, there it is,” Carey said, rolling her eyes.

The cacophony that ensued made it hard to understand what the two women were saying. Carey appeared to be talking about everyone being able to agree on the wonderfulness of her new shoes — also Louboutins, only strappier and not so high as Minaj’s and with little puffs at the toe.

Minaj, meanwhile, continued to discuss the merits of her sex tape as a peacekeeping device.

Finally, they appeared to run out of gas or at least remembered the media were in the room. Anyway, they stopped and caught their breath and let someone else on the panel speak.

Like exec producer Trish Kinane, who said they welcomed the vigorous (sometimes bodyguard-employing) give-and-take.

“We wanted judges who were experts and had a right to be here, and we also wanted honesty,” Kinane said, adding: “I think we’ve got it. They’re not shrinking violets — they say what they think, and we encourage that.”

Speaking of that, Minaj got asked about the trouble that rappers have had competing on “Idol.”

“I would never go on a show like this as a rapper,” she said. “I don’t think it’s authentic, and if you’re looking for people to believe you and see you as an authentic rapper, you wouldn’t do it.”